Universität Wien FIND

Due to the COVID-19 pandemic, changes to courses and exams may be necessary at short notice (e.g. cancellation of on-site teaching and conversion to online exams). Register for courses/exams via u:space, find out about the current status on u:find and on the moodle learning platform. NOTE: Courses where at least one unit is on-site are currently marked "on-site" in u:find.

Further information about on-site teaching and access tests can be found at https://studieren.univie.ac.at/en/info.

250105 VO Ergodic Theory (2020W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Thursday 01.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 06.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 08.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 13.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 15.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 20.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 22.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 27.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 29.10. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 03.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 05.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 10.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 12.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 17.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 19.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 24.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 26.11. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 01.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 03.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 10.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 15.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 17.12. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 07.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 12.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 14.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 19.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 21.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 26.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 28.01. 08:00 - 09:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

This is an introduction to ergodic theory, that is: the study of how invariant measures play a role in dynamical systems. Topics to be discussed are likely to include
- Invariant measures in various standard examples (both finite and infinite);
- Ergodicity, unique ergodicity and proving ergodicity;
- Poincaré recurrence and Kac' Lemma;
- Ergodic Theorems;
- Induced transformations, Rokhlin towers and similar results;
- Transfer operators;
- Connections to notions from Probability Theory (Mixing, Bernoulli processes).
The course will be given in English

Assessment and permitted materials

Oral examination (English but also possible in German)

Minimum requirements and assessment criteria

A fair understanding during the exam of the material covered during the course, specifically theorems, proofs or proof sketches, main examples and counter-example (to theorems if assumptions are missing)

Examination topics

The material covered in class (or if agreed a subset of this)

Reading list

There will be online classnotes. Background reading:
Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag 1975 ISBN 0-387-95152-0.
Ricardo Mañé, Ergodic theory and differentiable dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete 8. Springer-Verlag, Berlin, 1987. ISBN: 3-540-15278-4
Daniel Rudolph, Fundamentals of measurable dynamics, Oxford Science Publications, Clarendon Press Oxford 1990 ISBN 0-19-853572-4
Karl Petersen, Ergodic Theory, Cambridge Studies in Advanced Mathematics, 1983, Cambridge University Press ISBN 0-521-38997-6
Michael Brin and Garrett Stuck, Introduction to Dynamical Systems, Cambridge University Press 2002, ISBN 0-521-80841-3
Omri Sarig, Lecture Notes on Ergodic Theory Penn State, Fall 2008,

Association in the course directory

MSTV

Last modified: We 21.04.2021 12:28